Finite Group Databasebeta

← #13128847

Subgroups — #13128847

Order 1664.

1010 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#519C211yesmaximal, characteristic, complemented
2#11719522C211yesmaximal, characteristic, complemented
3Q8×C22⋊D13C211yesmaximal, characteristic, complemented
4#11719289C213yesmaximal, complemented
5#11719287C213yesmaximal, complemented
6#11719283C213yesmaximal, complemented
7#11719281C211yesmaximal, characteristic, complemented
8C4×#6131C211yesmaximal, characteristic, complemented
9#11719277C211yesmaximal, characteristic, complemented
10#11719273C213yesmaximal, complemented
11Q8×Dic26C211yesmaximal, characteristic, complemented
12#11719239C213yesmaximal, complemented
13#11719238C213yesmaximal, complemented
14#11719237C213yesmaximal, complemented
15#11719233C213yesmaximal, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×Q8×C13C2213yes—
21C4×Q8×C13C2211yescharacteristic
22C4×Q8×C13C2213yes—
23C13×#117C2213yes—
24C13×#117C2213yes—
25#88201C2213yes—
26#88200C2213yes—
27#88200C2213yes—
28Q8×Dic13C2211yescharacteristic
29Q8×Dic13C2211yescharacteristic
30#88198C2213yes—
31#88184C2213yes—
32C4×C22⋊D13C2213yes—
33C4×C22⋊D13C2213yes—
34#88178C2213yes—
35#88152C2213yes—
36#88152C2216yes—
37#88151C2213yes—
38#88150C2213yes—
39#88150C2216yes—
40#88149C2213yes—
41#88148C2213yes—
42#88147C2213yes—
43#88146C2213yes—
44#88146C2213yes—
45#88143C2213yes—
46#88142C2213yes—
47#88142C2213yes—
48#88141C2213yes—
49#88139C2211yescharacteristic
50#88139C2216yes—
51#88138C2213yes—
52#88137C2213yes—
53#88133C2213yes—
54#88130C2216yes—
55#88129C2216yes—
56#88129C2213yes—
57C4×D52C2213yes—
58C4×D52C2213yes—
59#88126C2213yes—
60#88126C2216yes—
61C42×D13C2213yes—
62#88123C2213yes—
63C4×Dic26C2213yes—
64C4×Dic26C2216yes—
65C4×Dic26C2213yes—
66C2×Q8×C13—24no—
67C2×Q8×C13C2313yes—
68C2×Q8×C13C2311yescharacteristic
69C22×C4×C13C2313yes—
70C2×C22⋊D13C2311yescharacteristic
71C2×C22⋊D13C2313yes—
72#6131—24no—
73Q8×D13—24no—
74C2×D52C2313yes—
75C2×D52C2313yes—
76C2×C4×D13C2313yes—
77C2×C4×D13C2313yes—
78C2×C4×D13C2313yes—
79C2×C4×D13C2313yes—
80C2×Dic26C2311yescharacteristic
81C2×Dic26C2313yes—
82C2×Dic26C2316yes—
83C13×C4⋊C4C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2313yes—
86C13×C4⋊C4C2313yes—
87C13×C22⋊C4C2313yes—
88C13×C22⋊C4C2311yescharacteristic
89C42×C13C2313yes—
90C42×C13C2313yes—
91C42×C13C2316yes—
92C22⋊Dic13C2311yescharacteristic
93C22⋊Dic13C2313yes—
94#6103C2311yescharacteristic
95#6103C2313yes—
96#6103C2316yes—
97#6103C2316yes—
98#6103C2311yescharacteristic
99#6103C2313yes—
100#6103C2316yes—
101#6103C2313yes—
102#6103C2313yes—
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2313yes—
107#6101C2313yes—
108#6101C2313yes—
109#6101C2313yes—
110#6101C2313yes—
111#6101C2316yes—
112#6101C2313yes—
113#6101C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2316yes—
116C4×Dic13C2313yes—
117C4×Dic13C2313yes—
118C4×Dic13C2311yescharacteristic
119#3518—131nomaximal, Sylow
120C23×C13C2411yescharacteristic
121C22×D13C2411yescharacteristic
122C22×D13C2413yes—
123Q8×C13—26no—
124Q8×C13#4114yes—
125C2×C4×C13—26no—
126C2×C4×C13C2413yes—
127C2×C4×C13C2411yescharacteristic
128C2×C4×C13C2413yes—
129C2×C4×C13C2413yes—
130C2×C4×C13C2411yescharacteristic
131C2×C4×C13C2413yes—
132C22⋊D13—22no—
133C22⋊D13—43no—
134C2×Dic13C2411yescharacteristic
135C2×Dic13C2411yescharacteristic
136C2×Dic13C2413yes—
137C2×Dic13C2413yes—
138C2×Dic13C2413yes—
139C2×Dic13C2411yescharacteristic
140D52—26no—
141D52—43no—
142C4×D13—26no—
143C4×D13—26no—
144C4×D13—26no—
145C4×D13—43no—
146Dic26—26no—
147Dic26—22no—
148Dic26—46no—
149Q82—131no—
150#556—133no—
151#556—133no—
152#556—133no—
153#555—133no—
154D4×Q8—131no—
155#548—131no—
156#548—131no—
157#542—133no—
158#542—133no—
159#533—133no—
160#529—133no—
161#519—131no—
162#519D1311yescharacteristic, complemented
163C4×#41—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13C2511yescharacteristic
168C2×D13—21no—
169C2×D13—23no—
170C2×D13—23no—
171C2×D13—21no—
172C2×D13—23no—
173C2×D13—21no—
174C4×C13—23no—
175C4×C13—21no—
176C4×C13—23no—
177C4×C13—23no—
178C4×C13—21no—
179C4×C13C2×#4116yes—
180Dic13—23no—
181Dic13—21no—
182Dic13—21no—
183Dic13—23no—
184Dic13—23no—
185Dic132−1+412yes—
186C2×#41—131no—
187C22×Q8—131no—
188C22×Q8C2×D1311yescharacteristic
189C4⋊Q8—133no—
190C4⋊Q8—133no—
191C4⋊Q8—133no—
192C4⋊Q8—133no—
193#126—133no—
194#126—136no—
195#126—133no—
196#126—136no—
197#125—133no—
198#124—133no—
199#124—131no—
200#124—136no—
201#124—133no—
202#124—136no—
203#123—133no—
204#123—133no—
205C22⋊Q8—133no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8—133no—
209C22⋊Q8—136no—
210C22⋊Q8—133no—
211#121—133no—
212#121—133no—
213#121—133no—
214C4×Q8—131no—
215C4×Q8—131no—
216C4×Q8—133no—
217C4×Q8—133no—
218C4×Q8—133no—
219C4×Q8—136no—
220C4×Q8C2×D1311yescharacteristic
221C4×Q8C2×D1313yes—
222C4×Q8C2×D1311yescharacteristic
223C4×Q8C2×D1313yes—
224C4×D4—133no—
225C4×D4—133no—
226C4×D4—133no—
227C4×D4—133no—
228C4×D4—133no—
229#117—133no—
230#117—133no—
231#117—133no—
232#117—136no—
233#117C2×D1313yes—
234#117C2×D1313yes—
235C2×C42—133no—
236C2×C13—41no—
237C2×C13C22×#4111yescharacteristic
238C2×C13C2×2−1+411yescharacteristic
239C2×C13#58511yescharacteristic
240D13—41no—
241D13—43no—
242#41—264no—
243C2×Q8—24no—
244C2×Q8—131no—
245C2×Q8—133no—
246C2×Q8—136no—
247C2×Q8—264no—
248C2×Q8C22×D1313yes—
249C2×Q8C22×D1311yescharacteristic
250C2×D4—131no—
251C2×D4—133no—
252C2×D4—133no—
253C2×D4—133no—
254C22×C4—133no—
255C22×C4—133no—
256C22×C4—133no—
257C22×C4—133no—
258C22×C4C22×D1313yes—
259C4⋊C4—133no—
260C4⋊C4—133no—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—133no—
264C4⋊C4—133no—
265C4⋊C4—133no—
266C4⋊C4—133no—
267C4⋊C4—136no—
268C4⋊C4—133no—
269C4⋊C4—133no—
270C4⋊C4C22×D1313yes—
271C4⋊C4C22×D1313yes—
272C4⋊C4C22×D1313yes—
273C4⋊C4C22×D1313yes—
274C22⋊C4—131no—
275C22⋊C4—133no—
276C22⋊C4—133no—
277C22⋊C4—131no—
278C22⋊C4—136no—
279C22⋊C4—136no—
280C22⋊C4—136no—
281C22⋊C4—131no—
282C22⋊C4—133no—
283C22⋊C4—133no—
284C22⋊C4—133no—
285C22⋊C4C22×D1313yes—
286C22⋊C4C22×D1311yescharacteristic
287C42—131no—
288C42—133no—
289C42—133no—
290C42—136no—
291C42—133no—
292C42C22×D1313yes—
293C42C22×D1316yes—
294C42C22×D1313yes—
295C13#351811yescharacteristic, complemented, Sylow
296C23—131no—
297C23—133no—
298C23C23×D1311yescharacteristic
299Q8—26no—
300Q8—262no—
301Q8—266no—
302Q8—526no—
303Q8#612714yes—
304D4—262no—
305D4—266no—
306D4—523no—
307D4—523no—
308C2×C4—26no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—133no—
313C2×C4—133no—
314C2×C4—133no—
315C2×C4—266no—
316C2×C4—266no—
317C2×C4—266no—
318C2×C4—523no—
319C2×C4C23×D1313yes—
320C2×C4C23×D1311yescharacteristic
321C2×C4C23×D1311yescharacteristic
322C2×C4C23×D1313yes—
323C2×C4C23×D1313yes—
324C2×C4C23×D1313yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—261no—
329C22—263no—
330C22—263no—
331C22—261no—
332C22—263no—
333C22—261no—
334C22C24×D1311yescharacteristic
335C4—23no—
336C4—23no—
337C4—21no—
338C4—21no—
339C4—23no—
340C4—132no—
341C4—261no—
342C4—263no—
343C4—261no—
344C4—263no—
345C4—263no—
346C4C2×#612716yes—
347C2—41no—
348C2—521no—
349C2—523no—
350C2C22×#612711yescharacteristic
351C2D13×2−1+411yescharacteristic
352C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#519C2
hypercenter#519D13
hypocenterC13#3518
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #519

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C13×#519C2semidirect
2. #11719522C2semidirect
3. Q8×C22⋊D13C2semidirect
4. #11719289C2semidirect
5. #11719287C2semidirect
6. #11719283C2semidirect
7. #11719281C2semidirect
8. C4×#6131C2semidirect
9. #11719277C2semidirect
10. #11719273C2semidirect
11. Q8×Dic26C2semidirect
12. #11719239C2semidirect
13. #11719238C2semidirect
14. #11719237C2semidirect
15. #11719233C2semidirect
162. #519D13semidirect
295. C13#3518semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#5192
#117195222
Q8×C22⋊D132
#117192892
#117192872
#117192832
#117192812
C4×#61312
#117192772
#117192732
Q8×Dic262
#117192392
#117192382
#117192372
#117192332
#351813